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Finding the Third Proportional to 1,780 and 3,647

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Solution

The third proportional to 1,780 and 3,647 is: 7,472.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,780 : 3,647 = 3,647 : x
  2. Step 2: Convert to fraction form
    1,780/3,647 = 3,647/x
  3. Step 3: Cross multiply
    1,780x = 3,647 × 3,647
  4. Step 4: Simplify right side
    1,780x = 13,300,609
  5. Step 5: Solve for x
    x = 13,300,609/1,780
  6. Step 6: Final answer
    x = 7,472.25

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.